(x-3)(x+1)=x*-11

Solution for (x-3)(x+1)=x*-11 equation:

Simplifying
(x + -3)(x + 1) = x * -11

Reorder the terms:
(-3 + x)(x + 1) = x * -11

Reorder the terms:
(-3 + x)(1 + x) = x * -11

Multiply (-3 + x) * (1 + x)
(-3(1 + x) + x(1 + x)) = x * -11
((1 * -3 + x * -3) + x(1 + x)) = x * -11
((-3 + -3x) + x(1 + x)) = x * -11
(-3 + -3x + (1 * x + x * x)) = x * -11
(-3 + -3x + (1x + x2)) = x * -11

Combine like terms: -3x + 1x = -2x
(-3 + -2x + x2) = x * -11

Reorder the terms for easier multiplication:
-3 + -2x + x2 = -11x

Solving
-3 + -2x + x2 = -11x

Solving for variable 'x'.

Reorder the terms:
-3 + -2x + 11x + x2 = -11x + 11x

Combine like terms: -2x + 11x = 9x
-3 + 9x + x2 = -11x + 11x

Combine like terms: -11x + 11x = 0
-3 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 9x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 9x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 9x + x2 = 0 + 3
9x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
9x + x2 = 3

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 3 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 3 + 20.25

Combine like terms: 3 + 20.25 = 23.25
20.25 + 9x + x2 = 23.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.82182538 and -4.82182538.

Subproblem 1
x + 4.5 = 4.82182538

Simplifying
x + 4.5 = 4.82182538

Reorder the terms:
4.5 + x = 4.82182538

Solving
4.5 + x = 4.82182538

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.82182538 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.82182538 + -4.5
x = 4.82182538 + -4.5

Combine like terms: 4.82182538 + -4.5 = 0.32182538
x = 0.32182538

Simplifying
x = 0.32182538

Subproblem 2
x + 4.5 = -4.82182538

Simplifying
x + 4.5 = -4.82182538

Reorder the terms:
4.5 + x = -4.82182538

Solving
4.5 + x = -4.82182538

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.82182538 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.82182538 + -4.5
x = -4.82182538 + -4.5

Combine like terms: -4.82182538 + -4.5 = -9.32182538
x = -9.32182538

Simplifying
x = -9.32182538

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.32182538, -9.32182538}